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Two milk-water solutions A and B are mixed in some ratio to get solution C. The concentration of milk in A, B and C is 30%, 40% and 50% respectively. In what ratio are A and B mixed?
- a)2 : 1
- b)1 : 2
- c)3 : 4
- d)Data inconsistent
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Two milk-water solutions A and B are mixed in some ratio to get soluti...
The concentration of milk in C is greater than the concentration of milk in both A and B, which is not possible.
Hence, the given data is inconsistent.
Hence, option 4.
Hence, the given data is inconsistent.
Hence, option 4.
Most Upvoted Answer
Two milk-water solutions A and B are mixed in some ratio to get soluti...
The concentration of milk in C is greater than the concentration of milk in both A and B, which is not possible.
Hence, the given data is inconsistent.
Hence, option 4.
Hence, the given data is inconsistent.
Hence, option 4.
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Community Answer
Two milk-water solutions A and B are mixed in some ratio to get soluti...
Understanding the Problem
To find the ratio in which solutions A and B are mixed to obtain solution C, we start by defining the concentrations:
- Solution A: 30% milk
- Solution B: 40% milk
- Solution C: 50% milk
Let the volumes of solutions A and B be 'a' and 'b' respectively.
Setting Up the Equation
The concentration of milk in the mixture (solution C) can be represented as follows:
Milk content in A = 0.3a
Milk content in B = 0.4b
Total milk content in C = Milk content in A + Milk content in B = 0.3a + 0.4b
The concentration of milk in solution C is given by:
(0.3a + 0.4b) / (a + b) = 0.5
Cross Multiplying
Cross multiplying gives:
0.3a + 0.4b = 0.5(a + b)
Expanding this equation results in:
0.3a + 0.4b = 0.5a + 0.5b
Rearranging the Equation
Rearranging leads to:
0.3a + 0.4b - 0.5a - 0.5b = 0
-0.2a - 0.1b = 0
This can be simplified to:
0.2a = 0.1b
=> a/b = 1/2
Conclusion: Ratio of A to B
The ratio of solutions A and B is 1:2. However, this contradicts the concentration of solution C. Since it is impossible to achieve a 50% concentration by mixing 30% and 40% solutions, it leads to the conclusion that the given data is inconsistent. Therefore, the correct answer is option 'D'.
To find the ratio in which solutions A and B are mixed to obtain solution C, we start by defining the concentrations:
- Solution A: 30% milk
- Solution B: 40% milk
- Solution C: 50% milk
Let the volumes of solutions A and B be 'a' and 'b' respectively.
Setting Up the Equation
The concentration of milk in the mixture (solution C) can be represented as follows:
Milk content in A = 0.3a
Milk content in B = 0.4b
Total milk content in C = Milk content in A + Milk content in B = 0.3a + 0.4b
The concentration of milk in solution C is given by:
(0.3a + 0.4b) / (a + b) = 0.5
Cross Multiplying
Cross multiplying gives:
0.3a + 0.4b = 0.5(a + b)
Expanding this equation results in:
0.3a + 0.4b = 0.5a + 0.5b
Rearranging the Equation
Rearranging leads to:
0.3a + 0.4b - 0.5a - 0.5b = 0
-0.2a - 0.1b = 0
This can be simplified to:
0.2a = 0.1b
=> a/b = 1/2
Conclusion: Ratio of A to B
The ratio of solutions A and B is 1:2. However, this contradicts the concentration of solution C. Since it is impossible to achieve a 50% concentration by mixing 30% and 40% solutions, it leads to the conclusion that the given data is inconsistent. Therefore, the correct answer is option 'D'.
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Two milk-water solutions A and B are mixed in some ratio to get solution C. The concentration of milk in A, B and C is 30%, 40% and 50% respectively. In what ratio are A and B mixed?a)2 : 1b)1 : 2c)3 : 4d)Data inconsistentCorrect answer is option 'D'. Can you explain this answer?
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